Extensivity and entropy current at thermodynamic equilibrium with acceleration

We derive a sufficient condition for the existence of the entropy current of a fluid at local thermodynamic equilibrium using relativistic quantum statistical mechanics, and put forward a general method to calculate it. We also work out a specific calculation in a non-trivial case of interest, namely a system at global thermodynamic equilibrium with proper acceleration of constant magnitude along the flow lines in Minkowski space–time, whose lowest possible proper temperature is the Unruh temperature. In this case, we show that the integral of the entropy current in the right Rindler wedge is the entanglement entropy with the left Rindler wedge.